WAEC Mathematics 2014 Objective — Question 44

Question 44 of 50 from the West African Examinations Council (WAEC) Mathematics 2014 Objective paper, with the correct answer and a full explanation.

In the diagram, O is the centre of the circle, line PR is a tangent to the circle at Q and ∠SOQ=86°. Calculate the value of ∠SQR°.

• A. 43°Correct
• B. 47°
• C. 54°
• D. 86°

Explanation

Since OQ⊥PR (radius to tangent) and triangle OQS is isosceles with ∠SOQ=86°, ∠OQS=(180°−86°)/2=47°. ∠SQR = 90°−47° = 43°.

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